Question

According to an estimate, the average age at first marriage for women in the United States was 26.1 years in 2010 (Time, March 21, 2011). A recent sample of 60 women from New Jersey who got married for the first time this year showed that their average age at first marriage was 27.2 years with a standard deviation of 3.5 years. Using a 2.5% significance level and the critical value approach, can you conclude that the average age for women in New Jersey who got married for the first time this year is higher than 26.1 years? Find the range for the p-value for this test. What will your conclusion be using this p-value range and α = .025?